Entanglement at a Two-Dimensional Quantum Critical Point: a Numerical Linked Cluster Expansion Study

Abstract

We develop a method to calculate the bipartite entanglement entropy of quantum models, in the thermodynamic limit, using a Numerical Linked Cluster Expansion (NLCE) involving only rectangular clusters. It is based on exact diagonalization of all n x m rectangular clusters at the interface between entangled subsystems A and B. We use it to obtain the Renyi entanglement entropy of the two-dimensional transverse field Ising model, for arbitrary real Renyi index alpha. Extrapolating these results as a function of the order of the calculation, we obtain universal pieces of the entanglement entropy associated with lines and corners at the quantum critical point. They show NLCE to be one of the few methods capable of accurately calculating universal properties of arbitrary Renyi entropies at higher dimensional critical points.

5 pages, 4 figures

References in corpus (10)

• A class of quantum many-body states that can be efficiently simulated
• Measuring entanglement entropy of a generic many-body system with a quantum switch
• Universal terms for the entanglement entropy in 2+1 dimensions
• Entanglement Entropy in the O(N) model
• Numerical Linked-Cluster Approach to Quantum Lattice Models
• Numerical Linked-Cluster Algorithms. I. Spin systems on square, triangular, and kagome lattices
• Measuring entanglement using quantum quenches
• Finite Size Scaling of Mutual Information: A Scalable Simulation
• Numerical Linked-Cluster Algorithms. II. t-J models on the square lattice
• Thermodynamic singularities in the entanglement entropy at a 2D quantum critical point

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